The study of coincidence, I believe, is fascinating in itself. But when you plumb the possibility of meaningful coincidences - Synchronicity, as it is known - you go beyond the fascinating into the uncanny.
Below is an old newspaper clipping I found. While the story it tells is easy enough to dismiss as mere coincidence, it yet proved to be an eerie prediction of the future.
At that same Pan-American Exposition in 1901 President William McKinley was cut down by assassin Leon Czolgosz. fulfilling the fireworks prediction; for when that tragic event occurred, the presidency fell to Vice-president Theodore Roosevelt.
Interestingly enough, just as the fireworks display gradually dissolved from Our Vice-President into Our President, President McKinley did not die at once after being shot but lingered on for a week. At that point Theodore Roosevelt was "Our President."